Method for calculating shape of painting spray head

ABSTRACT

A method for calculating a shape of a painting spray head that injects liquid paint supplied to the center in a radial direction while rotating, includes: inputting a material characteristic of painting liquid to be injected; selecting a start point where a curve starts on a front surface of the painting spray head; calculating the thickness of a liquid film injected from the painting spray head through an input numerical value; correcting the start point where the curve starts depending on a difference value between the calculated thickness of the liquid film and a required thickness of the liquid film; and calculating a curve shape of the painting spray head by using the corrected start point.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims under 35 U.S.C. §119(a) priority to and thebenefit of Korean Patent Application No. 10-2014-0025199 filed in theKorean Intellectual Property Office on Mar. 3, 2014, the entire contentsof which are incorporated herein by reference.

BACKGROUND

(a) Field of the Invention

The present invention relates to a shape calculation method of a sprayhead for painting which uniformly sprays paint onto the surface of avehicle body and uniformly forms a painted surface to improve aestheticcharacteristics of a vehicle body and maintain durability.

(b) Description of the Related Art

A technology using atomization of a liquid provides various benefits,e.g., the technology of a sprayer that sprays the liquid as very smallparticles can be used in different parts for various industries.

As a representative example, an atomization technology of the liquid isused as a primary technology in a fuel injection process and a paintingprocess. As compared to other technologies, a rotary spraying method isadvantageous in that fuel is sprayed by centrifugal force of a rotaryshaft, and as a result, a device is stable while a load of the device isless subject to injection pressure, and a system structure is simple andallows for miniaturization. The advantage of the rotary fuel injectionmethod provides the same advantageous method even in the case ofpainting.

An atomizer refers to a device that atomizes liquid to circularly spraythe atomized liquid in a spray pattern and is rotated at high speed. Theatomizer has an advantage in that all paint materials may be applied tothe atomizer, and such a device is suitable for an environment requiringlarge-scale painting such as continuous vehicle painting and thus iscontinuously performed.

According to an injection principle, liquid painting is supplied to thecenter of a rotated disk to be dispersed and sprayed around bycentrifugal force of the disk. In particular, when a rotational velocityand a liquid flow rate are controlled, a desired thickness of a liquidfilm may be obtained.

A bell cup may be fixed to the rotary shaft in a cone shape or a diskshape having a curve, and the paint is supplied to a back surface of thedisk and thereafter, is spread outside the disk as a thin film by thecentrifugal force of the disk that rotates at high speed.

In this case, the moment when the liquid deviates from the disk, theliquid is atomized by compressed air of a nozzle at an edge of the disk.A design of the spray head surface until the liquid is injected is themost important part in performance of the bell cup.

According to the design, painting quality is determined by the size of aliquid drop, and the size and the uniformity of the liquid drop dependon quality of a paint thin film formed on the surface of the bell cup bythe centrifugal force.

The edge may have a plane shape, a single sawtooth shape, or a crosssawtooth shape according to a spray head shape. The spray head is usedfor various paints, and as a result, various models and transformedproducts are required to satisfy requirements of performance andquality.

Important elements to determine the required models or transformedproducts are a diameter of the spray head, a disk material, an operationRPM, and an angle of a spray head surface.

The above information disclosed in this Background section is only forenhancement of understanding of the background of the invention andtherefore it may contain information that does not form the prior artthat is already known in this country to a person of ordinary skill inthe art.

SUMMARY

The present invention provides a shape calculation method of a sprayhead for painting that uniformly sprays paint onto the surface of avehicle body and uniformly forms a painted surface in an enhanced shapeto improve aesthetic characteristics of a vehicle body and maintaindurability.

An exemplary embodiment of the present invention provides a method forderiving a shape of a painting spray head that injects liquid paintsupplied to the center in a radial direction while rotating, including:inputting a material characteristic of painting liquid to be injected;selecting a start point where a curve starts on a front surface of thepainting spray head; calculating the thickness of a liquid film injectedfrom the painting spray head through an input numerical value;correcting the start point where the curve starts depending on adifference value between the calculated thickness of the liquid film anda required thickness of the liquid film; and calculating a curve shapeof the painting spray head by using the corrected start point.

The method may further include inputting an rpm of the painting sprayhead.

The material characteristic may include density and viscosity.

The method may further include selecting an injection flow rate of thepainting liquid.

The start point may is a linear distance measured toward an edge fromthe center of the painting spray head.

Another exemplary embodiment of the present invention provides apainting spray head which is manufactured by the method for calculatinga shape of a painting spray head; a painting liquid supplying unit whichsupplies painting liquid to the spray head; a compressed air supplyingunit which supplies compressed air to the spray head to inject thepainting liquid together with the compressed air; and a moving unitwhich moves the painting spray head along a set route of a set space.

A non-transitory computer readable medium containing programinstructions executed by a processor on a controller may include:program instructions that input a material characteristic of paintingliquid to be injected; program instructions that select a start pointwhere a curve starts on a front surface of a painting spray head;program instructions that calculate the thickness of a liquid filminjected from the painting spray head through an input numerical value;program instructions that correct the start point where the curve startsdepending on a difference value between the calculated thickness of theliquid film and a required thickness of the liquid film; and programinstructions that calculate a curve shape of the painting spray head byusing the corrected start point.

According to an exemplary embodiment of the present invention, paint isuniformly sprayed onto the surface of a vehicle body and a paintedsurface is uniformly formed in a more enhanced shape to improveaesthetic characteristics of a vehicle body and maintain improveddurability.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates the relationship of force in a spray head forpainting according to an exemplary embodiment of the present invention.

FIG. 2 illustrates liquid analysis of analyzing a forming height of aliquid film in the spray head according to the exemplary embodiment ofthe present invention.

FIG. 3 illustrates (a) force when there is no curve in the spray head,(b) force when a curve is formed at x0=1.5 cm, (c) a tangent rise angleat x0=1.5 cm, and (d) an actual profile (1:1) at x0=1.5 cm according tothe exemplary embodiment of the present invention.

FIG. 4 illustrates (a) a height distribution of a liquid film on a curvesurface based on 1.5 cm when (b) a flow rate of a non-dimensionalvelocity distribution is 440 cc and 25000 rpm when the liquid receivescentrifugal force on the surface constantly in the spray head accordingto the exemplary embodiment of the present invention.

FIG. 5 illustrates (a)-(b) a thin film thickness graph (1.0 to 3.5 cm)depending on a change of constant force and (c) a graph of a radius ofan approximate circle depending on constant force (1.0 to 2.0 cm) in thespray head according to the exemplary embodiment of the presentinvention.

FIG. 6 illustrates a process of making a smooth curve in the spray headaccording to the exemplary embodiment of the present invention.

FIG. 7 illustrates force calculated again for each radius of anapproximated circle in the spray head according to the exemplaryembodiment of the present invention, and illustrates (a) when there isno curve, (b) when a curve starts at 1.0 cm, (c) when the curve startsat 1.5 cm, and (d) when the curve starts at 2.0 cm.

FIG. 8 illustrates (a) final average force (1 to 2 cm), (b) a final filmthickness, and (c) a film thickness when water is used as the liquid inthe spray head according to the exemplary embodiment of the presentinvention.

FIG. 9 is a cross-sectional view of a spray head according to theexemplary embodiment of the present invention.

FIG. 10 is a front view of a painting spray head according to anexemplary embodiment of the present invention.

FIG. 11 is a schematic configuration diagram illustrating a paintingsystem including a painting spray head according to an exemplaryembodiment of the present invention.

FIG. 12 is a flowchart illustrating a sequence for manufacturing apainting spray head according to an exemplary embodiment of the presentinvention.

FIG. 13 is a schematic flowchart illustrating a process of a program formanufacturing a painting spray head according to an exemplary embodimentof the present invention.

FIG. 14 illustrates an input screen of a program for manufacturing apainting spray head according to an exemplary embodiment of the presentinvention.

FIG. 15 illustrates an execution result of a program for manufacturing apainting spray head according to an exemplary embodiment of the presentinvention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

An exemplary embodiment of the present invention will hereinafter bedescribed in detail with reference to the accompanying drawings.

It is understood that the term “vehicle” or “vehicular” or other similarterm as used herein is inclusive of motor vehicles in general such aspassenger automobiles including sports utility vehicles (SUV), buses,trucks, various commercial vehicles, watercraft including a variety ofboats and ships, aircraft, and the like, and includes hybrid vehicles,electric vehicles, plug-in hybrid electric vehicles, hydrogen-poweredvehicles and other alternative fuel vehicles (e.g. fuels derived fromresources other than petroleum). As referred to herein, a hybrid vehicleis a vehicle that has two or more sources of power, for example bothgasoline-powered and electric-powered vehicles.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a,” “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof. As used herein, the term “and/or”includes any and all combinations of one or more of the associatedlisted items.

Further, the control logic of the present invention may be embodied asnon-transitory computer readable media on a computer readable mediumcontaining executable program instructions executed by a processor,controller or the like. Examples of computer readable media include, butare not limited to, ROM, RAM, compact disc (CD)-ROMs, magnetic tapes,floppy disks, flash drives, smart cards and optical data storagedevices. The computer readable medium can also be distributed in networkcoupled computer systems so that the computer readable media is storedand executed in a distributed fashion, e.g., by a telematics server or aController Area Network (CAN).

FIG. 1 illustrates the relationship of force in a spray head forpainting according to an exemplary embodiment of the present invention.

Referring to FIG. 1, when an object rotates, centripetal force toward acircle center is generated according to a rotation radius r, an angularvelocity w, and a mass m.

The centripetal force is force which is the same as tension with which athread is pulled at the center so as to keep a predetermined rotaryradius when the object is tied to the thread. In addition, force to makethe object spring force by rotation is also generated, and the force iscalled centrifugal force.

The centripetal force and the centrifugal force are simultaneouslygenerated and when the centripetal force and the centrifugal force havethe same magnitude as each other, the object may be rotated with apredetermined radius. In this case, a relationship to acquire the forceis

$F = {F^{\prime} = {\frac{{mv}^{2}}{r} = {{mr}\mspace{11mu}{w^{2}.}}}}$

In particular, when there is no medium that holds the object, only thecentrifugal force is applied and the object moves in a radial directionwith acceleration.

It is assumed that predetermined force is applied from a radius x₀designed in FIG. 1 based on a given condition (m=0.1 kg, rpm=25,000rev/min, x>0 cm) in order to design the surface of the spray head.

The surface is changed to the curve from x₀ in order to apply thepredetermined force from the designated radius x₀. In this case, whenthe force at the radius x₀ is F₀, a component of tangent force for anentire curve is assumed as the predetermined force, and as a result, thetangent force is set to F₀.

Further, when radial force for x over the radius x₀ based on ahorizontal surface is F₀, a curve tangent angle a of point x based onhorizontality may be acquired through the relationship between F₀ andF_(x).

The relationship of a micro rise height dy for a microdistance dx isconsidered with respect to: which is an entire radius using the curvetangent angle, two surface functions illustrated below may be acquired.

${\left( {0 < x_{0} \leq 1} \right)\mspace{14mu} y} = \frac{x{\sqrt{1 - \left( \frac{x_{0}}{x} \right)^{2}}\left\lbrack {{x\sqrt{x^{2} - x_{0}^{2}}} - {x_{0}^{2}\left\{ {\ln\left( {x + \sqrt{x^{2} - x_{0}^{2}}} \right)} \right\}}} \right\rbrack}}{2\; x_{0}\sqrt{x^{2} - x_{0}^{2}}}$(x₀ > 1)  y^(′) = y + y(x₀)

In particular, since a particle need not be located at an origin inorder to receive centrifugal force, x₀>0 needs to be established. Insummary, in the case of the flow of the particle that follows twosurface functions, the particle flows along the surface while receivingthe same force as the force at the point where the curve is started andacceleration.

FIG. 2 illustrates liquid analysis of analyzing a forming height of aliquid film in the spray head according to the exemplary embodiment ofthe present invention.

In FIG. 2, when it is assumed that paint is sprayed in the form of athin film along the surface of the spray head by the centrifugal force,a cross-section of the flow may be analyzed as Couette flow having afree boundary surface as illustrated in FIG. 2 and it may be describedthat the paint has a predetermined acceleration by receiving apredetermined force on the curve.

Since a velocity component of the flow is present only in an x direction(u component),

$\frac{\delta\; u}{\delta\; x} = O$in a continuity equation and when the flow is regarded as a normal flow,u=u(y). In particular, when a Navier-Stockes equation is used, there isno acceleration of v and y and acceleration of w and z, and as a result,there is no pressure change of a y-z plane.

Since pressure on a film surface y=h is atmospheric pressure andpressure of an entire film is also atmospheric pressure (gauge pressureof 0),

$a = {{- \begin{matrix}\mu \\\rho\end{matrix}}\left( \frac{\delta^{2}u}{\delta\; y^{2}} \right)}$is shown as x-direction acceleration. When y is integrated and airresistance is disregarded at y=h, shear stress on the film surface is

${\tau_{yx} = {\mu\left( \frac{\delta\; u}{\delta\; y} \right)}},$and as a result, an integral constant may be acquired as

$C_{1} = {\frac{\rho\;{ah}}{\mu}.}$

By integrating y once more and substituting C₁, a velocity distributionis shown as

$u = {{{- \frac{\rho\; a}{2u}}y^{2}} + {\frac{\rho\;{ah}}{u}y}}$because u=0 when y=0. When the velocity distribution is integrated aslarge as h and a width b is calculated, a total flow rate is calculatedby

$q = \frac{\rho\;{ah}^{3}b}{3\mu}$and the thickness of the thin film is calculated by

$h = {\sqrt[3]{\frac{3q\;\mu}{\rho\;{ab}}}.}$

Herein, h represents the thickness of the liquid film, q represents aflow rate (cc), and μ (N*s/M²) and ρ (km/m²) represent a materialcharacteristic of painting liquid,

${a = {{- \frac{\mu}{\rho}}\left( \frac{\partial^{2}u}{\partial y^{2}} \right)}},$and in addition, referring to FIG. 1, b=2πx and b increases according tox.

Accordingly, an average flow rate q is Vhb and herein, an averagevelocity is

$V = {\frac{\rho\;{ah}^{3}}{3\;\mu}.}$A non-dimensional equation for the velocity distribution is

$\frac{u}{V} = {{- {C\left( \frac{y}{h} \right)}^{2}} + {2{C\left( \frac{y}{h} \right)}}}$and a non-dimensional coefficient is

$C = {\frac{\rho\;{ah}^{2}}{2\mu\; V}.}$

FIG. 3 illustrates (a) force when there is no curve in the spray head,(b) force when a curve is formed at x0=1.5 cm, (c) a tangent rise angleat x0=1.5 cm, and (d) an actual profile (1:1) at x0=1.5 cm according tothe exemplary embodiment of the present invention.

Modeling the surface by dynamical analysis is shown through a detailedgraph. A material used for the analysis is SAE 30 oil which is used asvehicular lubricating oil and a rotational velocity or a flow rate arepreset to table values.

In the case where a rotary radius increases from an original point whenthe paint rotates constantly at 25,000 rpm, it can be seen that thecentrifugal force increases proportionally through FIG. 3(a). When thesurface is the plane, the graph is illustrated as FIG. 3(a), but whenthe curve is added in order to acquire predetermined force, a form ofthe graph is shown as a graph to keep predetermined force at a specificpoint (1.5 cm) like FIG. 3(b).

The force increases proportionally according to a radius from theoriginal point to the specific point and the force shows a predeterminedaspect over the specific point. In order to keep the force constantly,the surface is curved and an angle formed by the tangent of the curveand the plane starts to be shown over the specific point like FIG. 3(c).

When the curve is started in an initial stage, the angle increasesrapidly and as the radius is larger, a sudden change does not occur, butthe angle with the surface is high. The constant force is acquired inFIG. 3(b) and the angle of the surface is acquired in order to keep theconstant force in FIG. 3(c).

The surface is formed as illustrated in FIG. 3(d) through the angle ofthe surface and a flat plate is maintained up to the specific point andthereafter, a curve having a small curvature is formed and as the radiusincreases, a curve having a large curvature is formed.

Accordingly, it may be determined that liquid that flows along thesurface on the same surface as the graph of FIG. 3(d) flows whilereceiving constant force up to the end of the curve from the specificpoint.

FIG. 4 illustrates a height distribution of a liquid film on a curvesurface based on 1.5 cm when (b) a flow rate of a non-dimensionalvelocity distribution is 440 cc and 25,000 rpm when the liquid receivescentrifugal force constantly on the surface in the spray head accordingto the exemplary embodiment of the present invention.

The flow on the surface determined according to a result of thedynamical analysis is described as the Couette flow of FIG. 2(B) thatflows along the curve while receiving the constant force through liquidanalysis and the velocity distribution of the material is illustrated inFIG. 4(A) according to the non-dimensional equation.

At the height of the surface and a proximate height, a velocity is shownto be low due to surface friction caused by viscosity of the material.On the contrary, since fiction does not almost affect a liquid film atwhich is a maximum height of the flow, and as a result, the velocity isshown to be highest. The material flows to the edge of the surface insuch a velocity distribution and is attached to the painted material andthe quality of painting depends on a particle atomization degree at thisend.

In FIG. 2, although the radius becomes larger, the flow rate that flowsper cylindrical cross section perpendicular to the surface needs to bemaintained constantly. The radius is increased for the flow at theconstant flow rate, whereas the height of a cylinder needs to bedecreased. FIG. 4(b) shows the thickness of the liquid filmcorresponding to the height of the cylinder from the specific point tothe end of the radius and shows a distribution in which the thickness ofthe liquid film is decreased and the thickness of the liquid film islowest at the end (x=3.5 cm).

FIG. 5 illustrates (a)-(b) a thin film thickness graph (1.0 to 3.5 cm)depending on a change of constant force and (c) a graph of a radius (1.0to 2.0 cm) of an approximate circle depending on constant force in thespray head according to the exemplary embodiment of the presentinvention.

The liquid film needs to keep a constant thickness or less of the liquidfilm in order to acquire desired painting quality. A desired liquid filmheight depends on constantly applied force.

In other words, the constantly applied force is different for eachspecific point separated from the original point and the end calculatesthe thickness of the final liquid film at the end as the liquid filmthickness is gradually decreased as illustrated in FIG. 4(B) accordingto the force.

An index is illustrated in FIG. 5(a)-(b), which indicates how largeconstant force is required to finally acquire the desired liquid filmthickness. Heretofore, the description is made by the curve illustratedin FIG. 3(d) by using a surface graph in order to maintain the constantforce.

However, a theoretical equation for applying the constant force at thespecific point is applied in the design, but when an actually designedequation is prepared in the drawing and the curve is actually processedwith an NC machine, there are a lot of problems in implementing acomplicated equation such as the surface graph. Therefore, the curve issimplified to a circle having a constant radius to be applied toprocessing.

A method for simplifying the curve is performed by as a method ofdrawing a circle in which radiuses from three predetermined points tothe center are the same by setting three predetermined points of thecircle by shaping a cross-section of the surface of the disktwo-dimensionally. First, an x value of a first point is a point wherethe curve separated from the original point is started and a y value is0.

An x value of a second point is an end point which is a maximum radiusand a y value is a value corresponding to an end point in the surfacegraph. Last, an x value of a third point corresponds to an intermediatevalue of a first x value and a second x value and a y value is a valueacquired by inserting the intermediate x value in the surface graph.

A surface radius proximate to the surface graph is illustrated in FIG.5(c) according to each constant force in an interval having a radius of1.0 to 2.0 cm. Accordingly, how large force is required to calculate thedesired thickness of the liquid film may be known through FIG. 5(a)-(b)and a radius of curvature requiring the force may be acquired throughFIG. 5(c).

FIG. 6 illustrates a process of making a smooth curve in the spray headaccording to the exemplary embodiment of the present invention.

When the curve is changed to the circle, the plane and the curve are notsmoothly connected around the specific point, but the surface isabruptly bent like point #1 of FIG. 6.

In this case, a phenomenon in which the material is significantly hitwhile flowing may occur. In order to prevent the phenomenon, a circularcurve (black) is further extended virtually and a lowermost portion ofan extended circle is caused to start from the specific point (point #1)to be smoothly connected with the plane.

When such a surface is obtained, the curve deviates from thedistribution of the force of FIG. 3(B) while the curve is lower than asurface profile of FIG. 3(D) and the liquid film thickness is alsoanalyzed to be different.

FIG. 7 illustrates force calculated again for each radius of anapproximated circle in the spray head according to the exemplaryembodiment of the present invention, and illustrates (a) when there isno curve, (b) when a curve starts at 1.0 cm, (c) when the curve startsat 1.5 cm, and (d) when the curve starts at 2.0 cm.

A distribution of force for each radius of the curve considering thesmooth plane is illustrated in FIG. 7. The same slope as a case in whichthere is no curve is shown before the curve starts, but an aspect of thegraph is gradually distributed in a form of the curve from the specificpoint where the curve starts.

It may seen that as the portion where the curve starts is estranged fromthe original point, the curve of the end is shown more distinctly andthe force at the end point is gradually decreased. It can be seen thatthe distribution of the force to be priorly constantly maintained isscattered while making the smooth surface through FIG. 7.

FIG. 8 illustrates (a) final average force (1 to 2 cm), (b) a final filmthickness, and (c) a film thickness when water is used as the liquid inthe spray head according to the exemplary embodiment of the presentinvention.

A case in which the distribution of the force which was constant isscattered, and as a result, it is difficult to analyze the filmthickness that acts under constant acceleration by the Couette flow isillustrated in FIG. 8(A) by acquiring average force of each of forcedistributions in FIG. 7.

It can be seen that although the curve start is changed while showingaverage force for the interval of 1 to 2 cm, the average force appliedto the liquid is not significantly changed. Since the average force isalmost similar, a final film thickness is not also changed asillustrated in FIG. 8(B). The thickness of water which is aqueous paintshows an almost similar final film thickness as illustrated in FIG.8(C).

Consequently, surface modeling considering revolution per minute (RPM),an angle of an injection surface, and surface affinity of the spray headis performed.

In the case of the flow of the particle that follows the surfaceequation acquired by the dynamical analysis, the particle flows alongthe surface while receiving the same force as the force at the pointwhere the curve is started and accelerated. The flow that flows on thesurface while receiving constant acceleration is analyzed as the Couetteflow to acquire the velocity distribution and particle atomization isshown by the thickness of the thin film discharged last.

It is difficult to actually prepare theoretical design equation such asthe surface equation in a design drawing and actually implementprocessing of the NC machine, and as a result, the curve is simplifiedto a circle proximate to the curve to be applied to the processing.Then, a point where a boundary is generated on the plane and the curveis made to be smooth and thereafter, the force distribution iscalculated with respect to the surface again.

While calculating the thickness of the film by the resulting averageforce, a final design of the spray head is completed. A conclusion isthat at any predetermined point appropriately separated from theoriginal point, a film thickness associated with the particleatomization to determine the performance of the spray head is almostsimilar, and the viscosity and the density of the liquid remarkably varywhen an appropriate curvature is given.

FIG. 9 is a cross-sectional view of a spray head according to theexemplary embodiment of the present invention.

Referring to FIG. 9, the spray head 900 has a supply hole for supplyingliquid paint at the center thereof. In addition, the spray head 900 hasa structure in which the spray head 900 rotates at a set velocity arounda rotary center axis of the center.

The liquid paint is characterized in that the liquid paint is injectedin a radial direction while moving from the center toward the edge of afront surface of the spray head 900 by the rotation of the spray head900.

In the exemplary embodiment of the present invention, an effect toimprove total durability and uniformly inject the liquid paint byoptimizing the shape of the front surface of the spray head 900 isachieved.

In the exemplary embodiment of the present invention, a product of thepainting spray head 900 requires an injection ability having dropletatomization of a predetermined degree or less.

A liquid film thickness above a front surface 905, a shape of a sawtooth(902 of FIG. 10) at the edge, and shaping air 910 complexly act onatomization performance of the head 900. In the exemplary embodiment ofthe present invention, the spray head 900 has an atomization levelhaving a droplet size which is ½ or ⅓ times larger than the liquid filmthickness by the action of the shape of the sawtooth 920 and the shapingair 910, and when the atomization level is proportionally converted, theheight h of painting liquid on the front surface 905 may be acquired.

FIG. 10 is a front view of a painting spray head according to anexemplary embodiment of the present invention.

Referring to FIG. 10, for example, when the sawtooth 920 and the shapingair 910 act on the atomization ½ times and 30 μm is required as adroplet size adsorbed in a painted surface, the height h of paintingliquid that flows along the front surface of the head may satisfy 60 μm.

Accordingly, an F value equivalent to the height h of the paintingliquid is calculated in FIG. 5(A) and thereafter, a radius R is setaccording to the F value in FIG. 5(B) and since the radius R is formedby a surface function y, x0 which is a point where the curve starts isselected through FIG. 5(C).

A method for calculating the shape of the painting spray head accordingto the present invention, which injects liquid paint supplied to thecenter in a radial direction while rotating, may include selecting aradial distance x from the center of the spray head, selecting adistance x0 where a slope surface starts at the radial distance from thecenter of the spray head, and setting a front form of the spray headthrough a predetermined equation described below.

${\left( {0 < x_{0} \leq 1} \right)\mspace{14mu} y} = \frac{x{\sqrt{1 - \left( \frac{x_{0}}{x} \right)^{2}}\left\lbrack {{x\sqrt{x^{2} - x_{0}^{2}}} - {x_{0}^{2}\left\{ {\ln\left( {x + \sqrt{x^{2} - x_{0}^{2}}} \right)} \right\}}} \right\rbrack}}{2x_{0}\sqrt{x^{2} - x_{0}^{2}}}$(x₀ > 1)  y^(′) = y + y(x₀)

The method may include selecting the thickness h of a liquid film on thesurface of the spray head, selecting a flow rate q of the paintingliquid, selecting material characteristics (μ (N*s/M2) and ρ (km/m2)) ofthe painting liquid, and calculating a position of an inflection pointwhere the slope surface starts through an equation described below byusing the selected characteristics.

$h = \sqrt[3]{\frac{3q\;\mu}{\rho\;{ab}}}$

Where,

$a = {{- \frac{\mu}{\rho}}\left( \frac{\partial^{2}u}{\partial y^{2}} \right)}$and b=2πx.

A painting system according to an exemplary embodiment of the presentinvention may include a control unit which performs the method forcalculating the shape of the painting spray head and the painting sprayhead.

The control unit may be implemented by one or more microprocessors thatoperate by a set program and the set program may include a series ofcommands for performing the method according to the exemplary embodimentof the present invention.

FIG. 11 is a schematic configuration diagram illustrating a paintingsystem including a painting spray head according to an exemplaryembodiment of the present invention.

Referring to FIG. 11, the painting system includes a vehicle 111, apainting spray head 900, a moving unit 113, a compressed air supplyingunit 115, and a paint liquid supplying unit 117.

The painting liquid supplying unit 117 supplies painting liquid of apredetermined amount to the spray head 900, the compressed air supplyingunit 115 supplies compressed air at set pressure to the spray head 900,and the spray head 900 injects the painting liquid on the surface of avehicle body through the painting liquid and the compressed air suppliedwhile rotating at a predetermined rotational velocity.

Moreover, the moving unit 113 moves the spray head 900 along a route setalong the surface of the vehicle body of the vehicle 111 to evenly coatthe surface of the vehicle body with the injected painting liquid. Acontrol unit (not illustrated) controls the elements according to a setprogram.

FIG. 12 is a flowchart illustrating a sequence for manufacturing apainting spray head according to an exemplary embodiment of the presentinvention.

Referring to FIG. 12, a method for manufacturing a painting spray headincludes selecting the density of a painting liquid (S120), selectingthe viscosity of the painting liquid (S122), selecting an injection flowrate of the painting liquid (S124), selecting a curve start point on acurve of a spray head 900 (S126), selecting an RPM of the spray head 900(S128), calculating the thickness of a liquid film injected from thespray head 900 (S130), comparing the calculated liquid film thicknessand a desired liquid film thickness (S132), correcting the curve startpoint according to a difference therebetween (S134), calculating a curveshape of the spray head 900 by using the corrected curve start point(S136), and actually manufacturing the spray head 900 according to thecalculated shape (S138).

A method for manufacturing a painting spray head may be performed by apredetermined program and the program may be executed by a system havinga processing ability such as a computer. Moreover, a cutting tool or aseparate mold may be used depending on a form of the spray headcalculated by the program or system.

In the exemplary embodiment, density and viscosity are considered as aproperty of painting liquid in S120 and S122, but a different propertymay be selectively used.

FIG. 13 is a schematic flowchart illustrating a process of a program formanufacturing a painting spray head according to an exemplary embodimentof the present invention.

Referring to FIG. 13, a virtual curve start point is input in stepS1300, a property value such as density or a coefficient of viscosity ofthe painting liquid (paint) is input in step S1310, and a flow rate andan RPM are input as an operating condition of the spray head (disk) 900in step S1320.

A height of the paint that is injected is calculated by the curve startpoint, the paint property value, and the operating condition of the diskwhich are virtually input through Equations 5 and 6.

Herein, the calculated height of the paint and a height desired by adesigner are compared to correct the curve start point.

The shape of the curve of the spray head 900 is set through thecorrected curve start point by using Equations 1, 2, 3, and 4 and avalue of a radius R depending on the position of the curve and predictedatomization, that is, the height of injected paint are calculated asoutput values in step S1330.

FIG. 14 illustrates an input screen of a program for manufacturing apainting spray head according to an exemplary embodiment of the presentinvention. FIG. 15 illustrates an execution result of a program formanufacturing a painting spray head according to an exemplary embodimentof the present invention. An input numerical value is expressed by thescreen of FIG. 14 and a calculated result is expressed by a screen ofFIG. 15.

While this invention has been described in connection with what ispresently considered to be practical exemplary embodiments, it is to beunderstood that the invention is not limited to the disclosedembodiments, but, on the contrary, is intended to cover variousmodifications and equivalent arrangements included within the spirit andscope of the appended claims.

What is claimed is:
 1. A method for calculating a shape of a paintingspray head that injects liquid paint supplied to the center in a radialdirection while rotating, the method comprising: inputting a materialcharacteristic of painting liquid to be injected; selecting a startpoint where a curve starts on a front surface of the painting sprayhead; calculating the thickness of a liquid film injected from thepainting spray head through an input numerical value; correcting thestart point where the curve starts depending on a difference valuebetween the calculated thickness of the liquid film and a requiredthickness of the liquid film; calculating a curve shape of the paintingspray head by using the corrected start point; and manufacturing thepainting spray head based on the calculated curve shape.
 2. The methodof claim 1, further comprising: inputting an rpm of the painting sprayhead.
 3. The method of claim 2, wherein: the material characteristicincludes density and viscosity.
 4. The method of claim 3, furthercomprising: selecting an injection flow rate of the painting liquid. 5.The method of claim 4, wherein: the start point is a linear distancemeasured toward an edge from the center of the painting spray head.
 6. Apainting system comprising: a painting spray head which is manufacturedby a method for calculating a shape of the painting spray headcomprising: inputting a material characteristic of painting liquid to beinjected; selecting a start point where a curve starts on a frontsurface of the painting spray head; calculating the thickness of aliquid film injected from the painting spray head through an inputnumerical value; correcting the start point where the curve startsdepending on a difference value between the calculated thickness of theliquid film and a required thickness of the liquid film; and calculatinga curve shape of the painting spray head by using the corrected startpoint.
 7. The painting system of claim 6, further comprising: a paintingliquid supplying unit which supplies painting liquid to the spray head;a compressed air supplying unit which supplies compressed air to thespray head to inject the painting liquid together with the compressedair; and a moving unit which moves the painting spray head along a setroute of a set space.